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Data reduction in storage systems is an effective solution to minimize the management cost of a data center. To maximize data-reduction efficiency, prior works propose post-deduplication delta-compression techniques that perform delta compression along with traditional data deduplication and lossless compression. Compared to the two traditional techniques, delta compression could be more effective because it can provide large data reduction even for non-duplicate and high-entropy data by exploiting the similarity within stored data blocks. Unfortunately, we observe that existing post-deduplication delta-compression techniques achieve significantly lower data-reduction ratios than the optimal due to their limited accuracy in identifying similar data blocks. In this paper, we propose DeepSketch, a new reference search technique for post-deduplication delta compression that leverages the learning-to-hash method to achieve higher accuracy in reference search for delta compression, thereby improving data-reduction efficiency. DeepSketch uses a deep neural network to extract a data block's sketch, an approximate data signature of the block that can preserve similarity with other blocks. Our evaluation using eleven real-world workloads shows that DeepSketch improves the data-reduction ratio by up to 33% (21% on average) over a state-of-the-art post-deduplication delta-compression technique.